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Llana [10]
3 years ago
5

In math class, there are 4 students to every 2 teachers. What is the ratio represented?

Mathematics
1 answer:
avanturin [10]3 years ago
6 0

Answer:

4 to 2

Step-by-step explanation:

you said it

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Which systems of equations have infinite solutions 2x+5y=31 6x-y=13 or 2x+y=10 -6x=3y+7 or y=14-2x 6x+3y=42 or y=13-2x 4x-3y=-19
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Answer:

  • y=14-2x; 6x+3y=42
  • 2x+y=17; -6x=3y-51

Step-by-step explanation:

Dependent equations will have infinite solutions. One way to tell if a system of equations is dependent is to put all of the equations into standard form. Here, we can use the form ...

  ax + by = c

where a, b, c are mutually prime integers and "a" is positive. When dependent equations are put in this form, they resolve to the same equation.

Here, the rearrangement is accomplished by putting the x- and y-terms on the same side of the equal sign, with the x-term having a positive coefficient. If necessary, the constant is put on the other side, and any common factors removed from all of them.

Then the sets of equations are ...

  • 2x +5y = 31
  • 6x -y = 13 . . . . not dependent

__

  • 2x +y = 10
  • 6x +3y = -7 . . . . not dependent

__

  • 2x +y = 14
  • 2x +y = 14 . . . . dependent

__

  • 2x +y = 13
  • 4x -3y = -19 . . . . not dependent

__

  • 2x +y = 14
  • x +2y = 13 . . . . not dependent

__

  • 2x +y = 17
  • 2x +y = 17 . . . . dependent

__

The 3rd and 5th sets of equations are dependent, so have infinite solutions.

_____

The second set of equations is inconsistent, so has no solutions.

6 0
4 years ago
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